Reasoning with Multiple-Agent Possibilistic Logic

  • Asma Belhadi
  • Didier Dubois
  • Faiza Khellaf-Haned
  • Henri Prade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9858)

Abstract

In multiple-agent logic, a formula is in the form of (aA) where a is a propositional formula and A is a subset of agents. It states that at least all agents in A believe that a is true. This paper presents a method of refutation for this logic, based on a general resolution principle and using a linear strategy, which is sound and complete. This strategy is then extended so as to deal with certainty levels. It manipulates formulas in the form \((a,\alpha /A)\) expressing that all agents in set A believe at least at some level \(\alpha \) that a is true. Finally, an experimental study is provided with the aim to estimate the performance of the proposed algorithms.

Keywords

Possibilistic logic Multiple-agent logic Multiple-agent possibilistic logic Possibility theory Refutation Uncertainty 

References

  1. 1.
    Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Multiple agent possibilistic logic. J. Appl. Non-Class. Logics 23(4), 299–320 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Reasoning about the opinions of groups of agents. In: 11th Europe Workshop on Multi-Agent Systems (EUMAS 2013), Toulouse, France, 12–13 December (2013). https://www.irit.fr/EUMAS2013/Papers/eumas2013_submission_68.pdf
  3. 3.
    Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Algorithme d’infrence pour la logique possibiliste multi-agents. In: Actes Rencontres francophones sur la logique floue et ses applications (LFA 2014), Cargese, France, 22–24 October, pp. 259–266. Cépaduès (2014)Google Scholar
  4. 4.
    Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Lalogique possibiliste multi-agents: Une introduction. In: Actes Rencontres francophones sur la logique floue et ses applications (LFA 2015), Poitiers, France, 5-6 November, pp. 271–278. Cépaduès (2015)Google Scholar
  5. 5.
    Dubois, D., Prade, H., Schockaert, S.: Stable models in generalized possibilistic logic. In: Brewka, G., Eiter, Th., McIlraith, S.A. (eds.) Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012), Roma, June 10–14, pp. 519–529. AAAI Press (2012)Google Scholar
  6. 6.
    Cholvy, L.: How strong can an agent believe reported information? In: Liu, W. (ed.) ECSQARU 2011. LNCS, vol. 6717, pp. 386–397. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Dubois, D., Lang, J., Prade, H.: Theorem proving under uncertainty - a possibility theory-based approach. In: McDermott, J.P. (ed.) Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI 1987), Milan, August, pp. 984–986. Morgan Kaufmann (1987)Google Scholar
  8. 8.
    Dubois D., Lang J., Prade H.: Possibilistic logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A., Nute, D. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press (1994)Google Scholar
  9. 9.
    Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets Syst. 144, 3–23 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Dubois D., Prade H.: Extensions multi-agents de la logique possibiliste. In: Proceedings of the Rencontres Francophones sur la Logique Floue et ses Applications (LFA 2006), Toulouse, 19–20 October, pp. 137–144. Cépaduès (2006)Google Scholar
  11. 11.
    Dubois, D., Prade, H.: Toward multiple-agent extensions of possibilistic logic. In: Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2007), London, 23–26 July, pp. 187–192 (2007)Google Scholar
  12. 12.
    Gutscher, A.: Reasoning with uncertain and conflicting opinions in open reputation systems. Electron. Notes Theor. Comput. Sci. 244, 67–79 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Asma Belhadi
    • 1
  • Didier Dubois
    • 2
  • Faiza Khellaf-Haned
    • 1
  • Henri Prade
    • 2
  1. 1.RIIMA, Université des Sciences et de la Technologie Houari BoumedieneBab EzzouarAlgeria
  2. 2.IRIT Université Paul SabatierToulouse Cedex 09France

Personalised recommendations